You can, except he says he spends the vast majority of his time doing engineering. There are lots of videos of him with a hardhat on working in his factories. Not PR videos, either. He's the head of product development for the cars, not just the CEO.
Hate the guy for his personality all you want; I can certainly understand why. But there's no need to downplay his achievements or skills.
Except the engineering work is usually not done with a hardhat on, "working" on the factory floor... that's production. I guarantee you if you see video of Elon Musk with a hard hat on doing anything other than touring the facility[1], it is marketing.
[1]Presumably, if he's down on the factory floor looking at things, he should be wearing a hard hat, so good for him. If he's bolting together cars himself, that's probably marketing.
He walks the factory floor every day wearing a hard hat, looking for process and tech improvements that could be made. He's not physically assembling the cars obviously. The engineering and design work is done in all of the meetings he's in every day, he says.
Hate the guy for his personality all you want; I can certainly understand why. But there's no need to downplay his achievements or skills.